Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

We propose a new reduced basis element-cum-component mode synthesis approach for
parametrized elliptic coercive partial differential equations. In the Offline stage we construct …

In the wind energy industry, a cost-benefit digital twin (DT) will be very useful for managing
the operation of a wind turbine. For instance, a DT could provide information on structural …

In this paper, robust preconditioners for multiscale flow problems are investigated. We
consider elliptic equations with highly varying coefficients. We design and analyze two-level …

We provide a concise review of the exponentially convergent multiscale finite element
method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without …

In this paper, we develop a component mode synthesis method that relies on artificial
springs to connect the subsystems of a built-up structure. The modal behaviour of the …

An improved neural networks method based on domain decomposition is proposed to solve
partial differential equations, which is an extension of the physics informed neural networks …

In this paper we propose local approximation spaces for localized model order reduction
procedures such as domain decomposition and multiscale methods. Those spaces are …

In this paper we introduce local approximation spaces for component-based static
condensation (sc) procedures that are optimal in the sense of Kolmogorov. To facilitate …

A robust two-level overlapping Schwarz method for scalar elliptic model problems with
highly varying coefficient functions is introduced. While the convergence of standard coarse …